A composite integer m is called a Lehmer number, or has the Lehmer property if phi(m) | m - 1, where phi(m) is the Euler function of m = A000010(m). According to the Grau and Luca reference's abstract they "show that there is no Cullen number with [the Lehmer property]". Hence, if phi (C_n) | C_n - 1, then C_n is prime. - Jonathan Vos Post, Mar 20 2011